Abstract

In the quantum system, perfect copying is impossible without prior
knowledge.
But, perfect copying is possible, if it is known that unknown states to
be copied is contained by the set of orthogonal states, which is called the
copied set.
However, if our operation is limited to local operations and classical
communications, this problem is not trivial.
Recently, F. Anselmi, A. Chefles and M.B. Plenio constructed theory of local
copying when the copied set consists of maximally entangled states.
They also classified the copied set when it consists of two orthogonal states
(quant-ph/0407168).
In this paper, we completely classify the copied set of local copying of the
maximally entangled states in the prime dimensional system.
That is, we prove that, in the prime dimensional system, the set of locally
copiable maximally entangled states is equivalent to the set of Simultaneously
Schmidt decomposable canonical form Bell states.
As a result, we conclude that local copying of maximally entangled states is
much more difficult than local discrimination at least in prime dimensional
systems.